Energy cost of entanglement extraction in complex quantum systems

TL;DR

This paper develops a theoretical framework to quantify the energy required to extract entanglement from complex quantum systems, introducing the concept of entanglement temperature and analyzing its behavior across different models and dimensions.

Contribution

It introduces a new theory for the energy cost of entanglement extraction, including the entanglement temperature, and applies it to various quantum models and field theories.

Findings

Energy cost depends on spatial dimension, growing exponentially in 1D systems.

Defined entanglement temperature relating energy cost to entanglement amount.

Numerical calculations of entanglement temperature in specific quantum models.

Abstract

What is the energy cost of extracting entanglement from complex quantum systems? In other words, given a state of a quantum system, how much energy does it cost to extract m EPR pairs? This is an important question, particularly for quantum field theories where the vacuum is generally highly entangled. Here we build a theory to understand the energy cost of entanglement extraction. First, we apply it to a toy model, and then we define the entanglement temperature, which relates the energy cost to the amount of extracted entanglement. Next, we give a physical argument to find the energy cost of entanglement extraction in some condensed matter and quantum field systems. The energy cost for those quantum field theories depends on the spatial dimension, and in one dimension, for example, it grows exponentially with the number of EPR pairs extracted. Next, we outline some approaches for bounding the energy cost of extracting entanglement in general quantum systems. Finally, we look at the antiferromagnetic Heisenberg and transverse field Ising models numerically to calculate the entanglement temperature using matrix product states.